On spherical unitary representations of groups of spheromorphisms of Bruhat–Tits trees

Yurii Neretin

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

Consider an infinite homogeneous tree $T_n$ of valence $n+1$, its group $Aut(T_n)$ of automorphisms, and the group $Hie(T_n)$ of its spheromorphisms (hierarchomorphisms), i.e., the group of homeomorphisms of the boundary of $T_n$ that locally coincide with transformations defined by automorphisms. We show that the subgroup $Aut(T_n)$ is spherical in $Hie(T_n)$, i.e., any irreducible unitary representation of $Hie(T_n)$ contains at most one $Aut(T_n)$-fixed vector. We present a combinatorial description of the space of double cosets of $Hie(T_n)$ with respect to $Aut(T_n)$ and construct a 'new' family of spherical representations of $Hie(T_n)$. We also show that the Thompson group has $PSL(2,Z)$-spherical unitary representations,
OriginalspracheEnglisch
Seiten (von - bis)801–824
Seitenumfang24
FachzeitschriftGroups, Geometry, and Dynamics
Jahrgang15
Ausgabenummer3
DOIs
PublikationsstatusVeröffentlicht - 2021

ÖFOS 2012

  • 101001 Algebra

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